At the general election of state and county officers, a member or members shall be elected for terms of six years to succeed the member or members whose term or terms of office expire at that time. The members of the county board of education shall hold office until their successors have been elected and qualified. Before exercising any authority or performing any duties as a member of the county board of education, each member thereof shall qualify by taking and subscribing to the oath of office prescribed by Article XVI of the state constitution, the certificate whereof shall be filed in the office of the judge of probate of the county.